For generations, first-grade students learned how to add using math tables and flashcards.
Carolyn Goehring employs plastic cubes and circles drawn in purple crayon. Rather than ask students to remember that five plus seven equals 12, the Raymond Chase Elementary School teacher wants them to visualize and illustrate different ways of getting there.
"The old way was based on memorization, and this is not," Goehring said in her classroom in Elk Grove. "This is meant to build a deep understanding of mathematics and to prepare them to be successful in higher-level math."
Goehring is among the earliest adopters of Common Core standards, a set of national guidelines that California and 44 other states have embraced as the next big shift in teaching.
The new standards stress critical thinking, problem solving and use of technology. Students will spend less time reading literature and more time analyzing nonfiction. Math lessons will teach students multiple ways to answer problems and apply skills to real-world situations.
California school districts are now hurriedly building curriculum, buying computers and training educators to teach to the new national standards. They have little time. State-mandated testing of the standards begins in 2014-15.
"This is the singular largest shift in public education in my nearly 25 years now," said Chris Evans, superintendent of Natomas Unified School District.
On a recent morning, Goehring gathered her students on the carpet. She pulled apart a string of plastic cubes and asked the students how many she held in each hand. "Five" and "seven," they answered.
"How do I show this on the board?" she asked. A student directed her to write "7 + 5."
Then Goehring drew a box and divided it into three parts, putting a 12 in the top box. She filled the bottom two boxes with a five and a seven at the direction of the students. The class repeated the exercise, this time putting a four and an eight in the bottom boxes.
Goehring finally showed them how to add by drawing circles in a grid of 10 squares.
After the lesson the students returned to their desks for practice. First-grader Natalie Galatioto pulled apart plastic links at her desk and counted aloud to eight as she drew purple circles with a crayon.
The methods are used to "develop mathematical thinkers," and prepare students for advanced courses that concentrate on things such as Base 10, the standard numbering system, said Anne Zeman, director of curriculum for the Elk Grove Unified School District. They are taught to think of the different methods as strategies, she said.
The Common Core standards also will find their way into social studies and history classes.
Students will have to know more than how to write a paper, said Gary Callahan, assistant superintendent at Roseville City Unified. "Now we will put you in a scenario to argue a different point and ask you to gather evidence to make the most compelling argument."
Annual standardized testing also will be dramatically different. One of the biggest changes: Students will use computers to take state-mandated tests known as smarter balance assessments.
The tests respond to the taker. They ask more difficult questions as students give correct answers and easier ones as students answer incorrectly.
"It adjusts and becomes more personal to the student," said Sue Stickel, Sacramento County deputy superintendent of schools. "We get a better picture of student knowledge from that."
She said the assessments will include open-response and performance-based questions, which require a student to complete a task or solve a problem, as well as some that rely on the traditional multiple-choice method.
The new tests may motivate reluctant teachers to teach toward the new standards, Stickel said. "Students are going to have to think on their feet," she said. "You know if I'm a teacher, I may have to change (the way I teach)."
Teachers brainstorm curriculum
In February, five teachers huddled around a horseshoe of tables with water bottles and coffee cups in an Elk Grove Unified conference room. They were building the curriculum needed to teach the district's 32,000 elementary school students English language arts.
"What we're creating today will be universal," said LaRae Blomquist, a curriculum specialist leading the group. "It hasn't been taught before."
The teachers brainstormed possible pitfalls in lesson plans. They worried that many students may be unable to summarize what they've read. They discussed the best way to teach students to analyze text.
They considered an example based on the "Three Little Pigs." Rather than recite the tale of pigs building houses out of straw, wood and brick, students will be expected to find themes in the book and locate evidence from the text to support arguments.
Cecilia Henry of Herberger Elementary warned against making the curriculum too rigid. "Teachers will either resist or stick rigidly to it," she said.
These are the sorts of discussions taking place across the country.
There are many hurdles. California schools have few materials to support the new guidelines. State lawmakers suspended textbook adoptions until the 2015-16 school year a year after students are scheduled to take the first mandated test under Common Core standards.
School districts also must find funds to pay for computers and the infrastructure to support the computer-assisted testing.
The districts, already subjected to years of budget cuts, do not expect additional state funding to carry out Common Core requirements, although Assembly Democrats this week proposed additional money.
The California Teachers Association supports the standards but has "serious reservations" about their implementation, said Dean Vogel, association president.
Districts need money and more time to implement the new standards, Vogel said. The state spent $10 billion to build assessments, train teachers and otherwise implement the standards adopted in 1997, he said.
American Federation of Teachers President Randi Weingarten last week asked the U.S. Department of Education to temporarily suspend penalties on schools that score poorly on tests until teachers and students can "master this new approach."
U.S. Secretary of Education Arne Duncan indicated last week in Palo Alto that his department could be flexible but isn't likely to offer an overall moratorium.
Despite the obstacles, Sacramento County school districts generally have done a good job of wading into Common Core, Stickel said. The Sacramento City, Elk Grove and San Juan Unified and Galt Elementary school districts are training teachers and beginning to use the standards in their classrooms.
National goals 'a great advantage'
The national standards were initiated by the Council of Chief State School Officers and the National Governors Association in 2009 to prepare students for the modern workforce and make them more competitive in a global marketplace.
Proponents also have touted the benefits of common nationwide educational goals.
"It's a great advantage," said Barbara Murchison, an administrator at the California Department of Education. "If New York is developing great things, we can share them. It is really unprecedented for us to have 45 states working together on this shared objective."
The blueprint was developed with input from teachers, content experts, leading thinkers and the public in 48 states and the District of Columbia, according to information from the state education department. In the end, 45 states adopted the optional standard.
Bill Evers, a research fellow at Stanford's Hoover Institute and a former U.S. assistant secretary of Education, is among those who oppose the new standards.
Evers said the math guidelines are mediocre and miss dozens of topics. Requiring students to take algebra in ninth grade rather than eighth "retards California's progress," he said.
He also questioned the "experimental" teaching methods in Common Core and said the "nationalization" of education will chill healthy competition between states.
"Instead of having the most challenging standards in the country and bringing kids up to a world-class level, our job is now to only do the same mediocre job expected of every other state," he said.
Lawmakers in several states have proposed bills to revoke participation in Common Core standards, fearing a loss of local control over education guidelines. The Republican National Committee passed an anti-Common Core resolution at its spring conference in Los Angeles a few weeks ago.
California's State Board of Education unanimously embraced Common Core standards in 2010 despite some concerns that they were weaker than existing requirements. Board members said the new standards would prioritize critical thinking instead and better prepare children for an economy dominated by information technology.
California first established standards for math and English in 1997, according to Murchison. The state's approval of the Common Core standards in 2010 was the first revision.
"Thirteen years is a long time," Murchison said. "Research continues to evolve. We now know more about effective teaching and learning than in 1997."
The California Department of Education still has much work to do. Officials there have built math guidelines but are still working on those for English, expected to be finished this month.
"This usually takes a couple of years, but we're doing it on an accelerated timeline," Murchison said.
Call The Bee's Diana Lambert, (916) 321-1090. Read her Report Card blog at http://blogs.sacbee.com/report-card/.