Akron algebra teachers spent a day away from their classrooms this month learning about a new way to teach math using words, not just numbers, to think out loud about math.


The group of nearly 45 high school and middle school teachers practiced talking through how they would solve math problems that their students might get on a test. They watched videos of other teachers getting their students to explain concepts in their own words, respond to their classmates' ideas, defend their own opinions with evidence and explain how they reasoned through a problem.


The district is paying the Institute for Learning at the University of Pittsburgh about $160,000 this year for five days of training for math teachers, literacy coaches and principals.


If the teachers were skeptical about yet another theory from the Ivory Tower about how to do their jobs, they were too polite to express it.


''I understand that there's this substantial skepticism when we come in,'' said Lauren B. Resnick, director of the Institute for Learning and an internationally recognized cognitive psychologist.


But she's convinced that the scientific evidence is strong enough now to share with teachers.


''We as a group of pretty hard-core scientists are convinced that we have real evidence now and we've gone public with it in the research world and it's being very well received,'' Resnick said. ''It's not just an idea whose time has come. It's an idea where there's finally enough evidence to have people like me who are skeptical say, 'Yeah, this is worth doing.' ''


Resnick began exploring the concept more than 20 years ago, when a Pittsburgh teacher told her about what she was doing in the classroom. Since then, the institute Resnick founded in 1995 has accumulated about 20 studies using a variety of methods that show gains for the students of teachers who are able to orchestrate these kinds of discussions.


For example, a series of studies in Britain that started in the 1990s showed that students whose teachers pressed them to explain solutions to science problems did better three years later on the national science exam for 15-year-olds. But they also did better on the math and English exams, Resnick said.


''You teach me to do this on a science problem and I get better in English three years later? That's not the only study that's shown this, but it's the largest one,'' Resnick said.


She thought the research would show that students would have to trade some fact knowledge in exchange for better reasoning skills, but she said that's not what the data say.


''We are not seeing lower scores on the knowledge tests anywhere among kids who have been taught this way,'' she said. ''I think that's a really big deal because up until six months ago, when we finally put all this evidence together, I thought we were going to have to make the case that there is a trade-off.''


The teaching technique is now called ''Accountable Talk,'' a registered trademark of the University of Pittsburgh.


''Accountable Talk'' means that students must be accountable to their fellow students, listening closely and paying attention to their ideas so they can build on them rather than just wait for their turn to talk. They must be accountable to the facts and use evidence to support their claims. And they must be accountable to sound reasoning about what those facts mean.


That's not what usually happens in classrooms, said Steve Miller, who oversees Akron's math instruction.


Miller believes the Institute for Learning's approach offers the most organized way to get students talking about concepts they'll have to master when the state fully implements new national math standards in 2014.


''The majority of time in classrooms, what I see is this model: The teacher shows, allows the students to practice, and then somewhere along the line, the students are expected to demonstrate what they have learned,'' Miller said.


That won't help students with Ohio's new ''common core'' math standards, which require them to explain why a mathematical statement is true rather than just memorize steps to arrive at an answer. They'll still have to learn the basic procedures, but they'll have to be able to explain their reasoning as well, Miller said.


During the one-day training this month, Institute for Learning instructor LuAnn Malik gave the algebra teachers a typical story problem their students might have to solve: Alazar Electric Co. sells light bulbs to big-box stores and every sample of 96 includes four defective bulbs. Today's batch is 6,000 bulbs and it has the same proportion of bad bulbs. How many are defective?


Students are traditionally taught a procedural shortcut to solve the problem called cross-multiplication, which involves following a series of memorized steps to get the answer: 6,000 times four divided by 96 equals 250.


''If you solve this problem by cross-multiplication, that's fine, but I want you to do it another way,'' Malik said.


But the shortcut, while useful, doesn't tell students anything about the deeper mathematical concepts that will be on the test.


''When you look at the common core state standards for grades six and seven, you are not going to see cross-multiplication mentioned,'' Malik said.


Some used tables to show the relationship between the good bulbs and the defective ones. Others imagined breaking up the total amount of 6,000 into individual boxes of 23 good bulbs for every one bad bulb. She pressed them to talk out loud about the reasoning they used to get the answer because their students will have to do that to pass the tests.


She told them she didn't expect them to master the technique in a day.


''That's a hard skill to build and it really takes diligence and practice over time to make that happen,'' Malik said.


Education reform


The Institute of Learning has worked with almost 70 school districts throughout the country on reforms that all include ''Accountable Talk'' training.


The Akron workshop featured a short video presentation by Resnick.


''The basic idea is that the more you manipulate the pieces of knowledge, the better you understand them, the better you remember them, the more complex your memories become and the smarter you get,'' Resnick said.


The Institute for Learning is working with districts such as Akron to perfect the techniques on a larger scale.


''I am now convinced, and I think much of the field is convinced now, that this works if you can get teachers to do it,'' she said. ''We know that teachers who do it get a result, but we're still working on how to do the training.''


Resnick also works with the Pittsburgh Science of Learning Center, one of six centers around the country funded by the National Science Foundation to support fundamental research about how people, other animals and machines learn.


Soo-Siang Lim, program director of the Science of Learning Centers Program at the foundation, said Resnick has worked for many years researching how ''Accountable Talk'' promotes learning.


''She's the world-renowned expert on this,'' Lim said.


The Science and Learning Centers hope to provide teachers and policymakers with scientific evidence, which often is missing in ideological debates about how to ''fix'' education.


''It seems that education reform has been quite cyclical and has reached its limits,'' Lim said. ''We believe that this integrative, science-based knowledge of how people learn should contribute to that discussion to inform education interventions, and to better design technologies that can enhance learning.''


But the work requires better connections between researchers and teachers, Lim said.


''You want the teachers to be involved in such a way that they understand what that new evidence is, in order to decide whether it is useful and how it is useful,'' she said. ''We're always very concerned of instances where people take something and think it's a magic bullet.''


John Higgins can be reached at 330-996-3792 or jhiggins@thebeaconjournal.com. Read the education blog at http://education.ohio.com/.