It was time for math in Abby Shink’s third grade class, but instead of pulling out pencils and workbooks, the students gathered on the carpet to talk things out.

Shink wrote a simple addition problem, 33 plus 57, on a large notepad for her students to solve in their heads. Students quickly raised their thumbs to show they’d figured it out, and Shink called on one after another to explain their solutions. All of them had the right answer, 90, but what Shink was really after was the process, the “how.”

A “number talk” like this one Shink led in the fall is one example of ways that discussion and writing have become a bigger part of math lessons since Readfield Elementary and its district, Regional School Unit 38, started implementing the Common Core State Standards.

Teachers in RSU 38 and other districts across Maine and the country are adapting instruction for the Common Core, a set of expectations for what students should learn in math and English at each grade level. The standards are supposed to help prepare students for college and the workforce by teaching them to learn independently, analyze information and communicate clearly.

The math standards, for example, say that students at every grade level should be able to construct an argument about why something is correct and critique the reasoning of others, and by the end of third grade they’re supposed to fluently add and subtract numbers up to 1,000.

So as one stone on the path to meeting those standards, Shink gave her students 33 plus 57.

Some students said they swapped the order of the numbers to make it easier to count up by 10s, which they’d just learned was allowable based on the commutative property of addition. Using strategies learned in earlier grades, they broke down the numbers in different ways, so that some added 30 and 50, then 3 and 7, while others added 33 and 7 to make 40, then the remaining 50.

Every time a student presented a solution, Shink encouraged the others to say whether they agreed or disagreed, and why.

Students are encouraged to find different strategies to solve a problem. The traditional algorithms, such as stacking one number on top of another and carrying the ones, are supposed to come later, after students have come to understand the mechanics behind the math.

The Common Core has drawn fierce opposition in some places, including a petition to repeal the standards by voter referendum in Maine, but Shink said what little resistance she’s encountered has been a result of parents missing the familiar algorithms and memorization in their children’s homework.

“I’ve had a few parents say, ‘Why are you not just teaching them this way? This is how I learned it,’” Shink said. “Usually when we talk about it and I explain it, they’re fine.

“I say that the way that we’re teaching it now, I think that kids have a much deeper understanding of numbers and they are much more flexible thinkers about how numbers can be put together and taken apart. And that they’re thinking a lot more creatively about how to solve problems and show their thinking and explain what they’ve done.”

New national standard

Maine formally adopted the Common Core State Standards in 2011, launching school districts on a multiyear process to understand the standards and adapt to them.

The current school year is supposed to be the year of full implementation, and the impact is becoming apparent in homework assignments, reading lists and the words teachers use when talking with students.

The District of Columbia and 45 states have adopted the stanards, which were developed to address the problem of low expectations in the academic standards of many states. The new standards were designed to be rigorous enough that all students graduating from high school will be ready for college or the workforce.

Maine State Chamber of Commerce President Dana Connors said Maine and the nation needed up-to-date standards in order to be globally competitive.

“That’s what this effort is, is to try to raise the level of standard, to prepare our people as well as our economy to compete at that level,” Connors said.

The Common Core is not a curriculum, but a set of statements about what students should be able to do by the end of each grade.

“There’s nothing in the standards themselves that dictates the way you teach them,” Regional School Unit 38 math coach Sarah Caban said.

RSU 38 literacy coach Barbara Bourgoine agreed.

“The standards are what you have to teach,” she said, “and our job is to figure out how.”

After Maine adopted the Common Core, educators in local school districts got to work examining the standards, identifying gaps in what they were already doing and training teachers in new approaches to familiar subjects. In some districts, Common Core work has dominated professional development time for the past year or two.

Some school districts are closer to the goal of full implementation than others, but even in a district like RSU 38 that started changing instruction last year, educators say it’s an ongoing process.

Katie Joseph, curriculum director for Gardiner-based RSU 11, said that district is still doing a lot of behind-the-scenes curriculum work, exploring possibilities for a new elementary math program and piloting new textbooks in middle school social studies and high school English.

“We’re at the cusp of starting a lot of different things,” Joseph said. “When we get there, I think students will be provided a really high-quality education that does prepare them for careers.”

Becky Armstrong said she believes the Common Core is helping her daughter, Manchester Elementary first grader Zion Armstrong, gain a deeper understanding of math. She’s hopeful that it will put Zion in a better position than the adults Armstrong teaches in Winthrop, who have forgotten the math facts they learned by rote years ago.

Armstrong said her daughter is also responding well to the literacy standards, which she said set higher expectations than she remembers from school.

“I think my teacher was happy that I read the words, and she’s got more of a reading comprehension focus,” Armstrong said. “I notice her try harder books, and I think as a child I would have been intimidated by something with more complex reading because I hadn’t got to that level. She just tries to read everything.”

Common Core opponent Heidi Sampson, a member of the State Board of Education, argues that the math standards are both too advanced at the lower grades, introducing abstract concepts too early, and too weak in the upper grades, leaving little or no time for calculus in high school. She’s also concerned by the reduction in nonfiction reading called for in the English language arts standards.

Sampson, who lives in Alfred and homeschooled her children, co-founded No Common Core Maine, a group that advocates ditching the standards.

“We need to see standards in Maine that belong to Maine, that we can control, that are not copyrighted, that we can add to, change, tweak, adjust, that are genuine high-quality standards, and rely on some people who actually know what they’re doing,” she said.

Critics of the Common Core worry that standards that were not developed in Maine will dictate what happens in classrooms here. They contend that teachers will be beholden to curriculum materials that are reworked for the Common Core and the Core-aligned tests that Maine and 21 other states will start using in 2014-15.

“I’m sorry, but standards will drive the curriculum toward the assessment that’s going to be given on the other end,” Sampson said.

Local teachers and administrators say that they haven’t had to buy many new materials yet, that they have flexibility in how they teach and that the changes they’ve made in response to the standards will make students better learners, not just better test-takers.

Real life scenarios

In math, the content standards are accompanied by a set of eight mathematical practice standards that apply at all grade levels and are supposed to help students think about and understand numbers and math more deeply.

One mathematical practice standard says students should learn to find patterns or structure in math and apply them to new problems or concepts.

Another says students should model with mathematics, using what they’re learning to solve problems or questions in everyday life.

Cony High School math department chairwoman Pat Hannigan said in the past, algebra students often were assigned to solve equations using rules and steps they’d memorized without perhaps understanding them thoroughly.

Now a teacher is more likely to give students a real-life scenario with several components — involving, say, the cost of car ownership with gas, car payments, insurance and the like — and task the students to set up and solve the equation on their own.

The high school math standards are not specific to any grade or course, in order to give high schools flexibility in organizing the standards into a course sequence.

So although the standards do not call by name for a precalculus course, all students are expected to learn concepts and skills that have typically been taught in precalculus, which is not a requirement at most local high schools.

That’s the case at Cony High School, where the math department has responded by incorporating more standards into the existing mandatory course sequence of Algebra I, Geometry and Algebra II.

“We’re trying to get more meat into those courses so the students have more under their belts,” Hannigan said.

That will mean more trigonometry in geometry classes and a deeper dive into topics such as polynomial expressions and exponential functions that have been covered at a more basic level in Algebra II.

To make room for those additions, other content is being pushed down from Algebra II to Algebra I, and from Algebra I to eighth grade. The Common Core requires some of this.

The standards start incorporating algebraic equations in sixth grade, requiring students to derive expressions from real-world problems and understand and use variables to represent numbers.

By eighth grade, students must be able to solve linear equations, which Hannigan said might not have been covered until late in Algebra I in the past.

The Common Core standards also require students to learn more about statistics and probability.

To help students meet those standards, Cony staff have designed a half-credit statistics course, which they’ll present soon to the Augusta school board. The course may become mandatory for students, starting with next year’s freshmen.

The changes happening in Augusta are likely to be similar to those elsewhere in Maine. Although some schools do offer Algebra I for eighth graders, only 23 percent of eighth graders in the state took algebra in 2007. And most high schools are like Cony in requiring only three years of math, topping out at Algebra II, though most recommend a fourth year of math to prepare for college and keep skills sharp.

Hannigan said math instruction at Cony is still evolving in response to the Common Core. Even more than other subjects, math builds from one concept to the next, creating difficulties if a student has a gap in a particular area, so the transition at the high school level is affected by the implementation still ongoing in the lower grades.

“We know what needs to be taught, but I can’t say everything is being implemented at this time,” Hannigan said. “What we do depends on K-8 as well. If they are doing more conceptual learning in K-8, they’re going to come to us with more under their belts than they have been.”

Ready for college and work

The English and language arts standards call for students to read much more nonfiction, particularly in high school. Reading materials should be 50 percent nonfiction in elementary school, the standards say, increasing to 70 percent in high school because nonfiction is most of what the students will have to read in their professional lives.

Those figures encompass the reading students do across all subjects, so science and social studies classes should make up most of the necessary nonfiction. Students at Cony High School are doing more reading and writing in all of their classes, English department Chairman Tom Wells said, but they still wouldn’t reach the 70 percent threshold without adding more nonfiction in English classes.

Wells said some teachers were dismayed at having to remove novels they’d taught for years.

“Originally, because we didn’t understand it quite as deeply as we do now, there was great resistance without a doubt,” he said. “But when we looked at our curriculum and factored in other subjects, it didn’t change things dramatically.”

Wells said the Common Core has been a good thing for reading lists because it sets a high bar for reading comprehension and analytical skills, leading teachers to add more challenging texts, both fiction and nonfiction.

Cony teacher Laurie Rodrigue, for example, bought “The Bedford Reader,” a college composition text consisting largely of nonfiction essays and academic writing for students to analyze, as well as some fiction, like Shirley Jackson’s classic short story “The Lottery.”

“The Bedford Reader” has replaced some of the easier classics that Rodrigue has typically taught, such as the modern English translations of “Beowulf” and “The Canterbury Tales.”

The emphasis on fact and argument in reading assignments also carries over to the writing standards in the Common Core. While students still write about personal thoughts and experiences on occasion, more often they’re expected to synthesize information and write persuasively, as they might need to for a college term paper or a report for an employer.

Joseph, RSU 11′s curriculum director, said the difference was evident in a comparison she recently came across between a 2013 SAT essay prompt and a sample task from the Smarter Balanced Assessment Consortium, which is developing the tests Maine will start using in 2015.

The SAT prompt asked students to argue whether happiness is a good measure of personal wisdom, using examples from their studies or lives.

“The old SAT question asks students to basically provide their point of view, but they’re allowed to support that with their own experience or observations, whereas the new task has them assessing different sources, arguing whether a nuclear power plant would be OK,” Joseph said. “They’re put in a position where they’re supposed to give a report to a congresswoman that they’re working for, which is something they could actually do for a career.”

Writing assignments about real-world scenarios have crossed over into English classes, taking a place alongside the writing about literature that students have traditionally done.

In a common assignment in Wells’ classes, he gives students seven sources — including newspaper or magazine articles, op-eds, political cartoons or charts and graphs — providing a variety of perspectives on a topic, such as global warming. Students must take a position on the topic, then back up their argument using three to five of the sources, which they must also cite in Modern Language Association format, a common requirement for college papers.

Related standards reach down into the earliest grades to prepare students for the expectations they’ll face by high school.

Manchester Elementary School teacher Jessica Gurney’s first graders spent only the first third of the year on narrative writing, which she said used to make up nearly all the writing by students at that level.

Like usual, she had her students start this year by writing stories, but then she introduced them to informational writing in the fall. During the last trimester of the year, they’ll write opinion pieces.

At the start of the unit on informational writing, Gurney read a series of nonfiction books with her class as examples, like a book about bones that connected to their science lessons about skeletons. Then she assigned them to write and illustrate a book to teach others about a topic they know well.

Students chose topics like horses, trucks and fishing. Faith DiFazio’s book, about how to hold a cat, included steps such as asking parents for permission and washing one’s hands.

Gurney had all the students check off whether their books showed that they’d learned what they were supposed to, such as whether they’d included facts in their writing and had written an ending.

Since introducing the Common Core, teachers in RSU 38 are holding students more responsible for knowing their learning goals and evaluating their work against those goals. They also seek to motivate students with a healthy dose of encouragement to persevere through challenges — teachers call their students mathematicians during math lessons and authors when they’re writing.

“This was our very first time writing a brand new type of writing,” Gurney told her class before moving on to the next subject. “It was hard, and it was tricky. But it was fun, and you are so good at it.”

RSU 11 teachers also are making learning targets more tangible for students, rewriting them as “I can” statements and talking with students about them daily. Joseph said that’s one of the district’s most visible changes at the classroom level as a result of the Common Core.

Eventually, the need to have each student reach every standard will require students, rather than teachers, to lead what happens in classrooms, Joseph said.

“I’m really excited about the level of critical thinking and self-directed work that they require students be able to do,” Joseph said. “I do think in the end that these standards are going to create students who are more college and career ready, which is the point.”

Susan McMillan — 621-5645 smcmillan@centralmaine.com Twitter: @s_e_mcmillan