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 RFID tag and asked the students how many she held in each hand. "Five" and "seven," they answered.
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.
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.
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."
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