The seventh-grade boy looked down at his blank work sheet, unsure how to begin solving the multistep algebraic equation that the teacher had written on the white board.
After a moment's hesitation, he began building the equation, X + -2 = -6, with blue and white tiles sitting atop his work sheet to find the mysterious value of X.
After manipulating the tiles, he thought he had the answer. However, after a second look he quickly corrected himself, earning a nod of approval from his Costa Mesa Middle School math teacher, Racine Cross.
Although he wasn't correct the first time — the answer was -4 — the lesson was a success in the eyes of the educators in the room.
"These lessons encourage them to be wrong and then work together with the teacher to find the right answer," said Steve McLaughlin, the director of secondary curriculum and instruction for the Newport-Mesa Unified School District. "I've seen too many kids check out for fear of failure."
Teachers at the district's middle schools are implementing a new hands-on approach to learning math in the classroom this year — lessons that will find their way into the district's high schools by next year.
The lessons, which were created and tested by Newport-Mesa teachers, align with the new state-mandated Common Core standards, which emphasize real-life applications of classroom material and encourage students to think critically about what they're learning.
The middle school math curriculum changes this year are a trial run for the district. Next year teachers will begin implementing the new math standards in the district's high schools, beginning what they refer to as a "pathway."
During a recent board meeting, trustees approved new sets of classes in the pathway that will be available for middle and high school students in the coming years.
What was once referred to as Pre-Algebra, Algebra 1, Geometry and Algebra 2 will take on fresh names and involve innovative curriculum, according to a presentation by district officials.
The standard pathway starts with a class called Math 7 in seventh grade, which includes elements of pre-algebra. The pathway takes students through additional math classes, ending at pre-calculus during their senior year.
Students who are more advanced in math have the option to start out in a class called Enhanced Math 8, which includes material taught in Math 7, but at a faster pace. Those students have the ability to take either AP Calculus or AP Statistics their junior and senior years.
Lessons in concepts like algebra and geometry will be blended in the classes, instead of being separated out into specific courses during a student's high school years. This will give students a better understanding of how the concepts connect with one another, officials said.
Throughout the standard pathway, students can test into the enhanced classes with a teacher's recommendation. They can also return to the basic-level classes if the enhanced classes are too difficult.
Districts across the state are transitioning their curriculum to align with recently implemented Common Core standards. Those who are skeptical of Common Core often believe the curriculum is being developed by federal or state officials, but McLaughlin has set out to prove that's not the case.
"We consistently emphasize that we're making it our own and allowing teachers to develop the curriculum we're using," McLaughlin said.
Newport-Mesa teachers are working with the UC Irvine Math Project, a collaboration among the university and local school districts, to create the new Common Core math curriculum.
The majority of college professors say that fewer than 20% of their students were prepared for college-level math courses, said Karajean Hyde, a lecturer at UC Irvine who is part of the math project.
District officials believe the pathway classes and curriculum will change that statistic.
"Newport-Mesa is surpassing almost every other district we're working with in readiness and being ahead of the game for Common Core," Hyde said.
For students in Newport-Mesa Unified middle schools this year, math classes aren't filled with slide show presentations, endless formulas and questions in textbooks, as in years past.
This year, middle school math teachers traded their PowerPoint presentations for pattern blocks and their textbook questions for colorful algebra tiles to teach basic algebra concepts like solving equations and writing expressions.
This new approach to learning is different from regurgitating passages of textbooks during exams and answering questions without understanding how they got the answer, teachers say.
"With these lessons they're able to visualize what they're learning," said former Costa Mesa High School Principal Phil D'Agostino, now a district administrator. "Kids retain information better when they can manipulate with their hands."
During a recent lesson in a Math 7 class at Ensign Intermediate School in Newport Beach, Nadine Velastegui used pattern blocks to teach her seventh-grade class how to write algebraic expressions and analyze which variables can be combined to simplify the expression.
After a quick explanation, the students were able to work in groups to build designs with the pattern blocks in order to create a mathematical expression. The hands-on approach is something Velastegui says she values about the new standards.
"Growing up learning math, teachers never explained why we do things the way we do," she said. "Now, these students are developing the why and understanding the whole concept of the math they're learning."
Cierra Bird, a seventh-grader at Ensign, said the in-class exercises help reinforce what she reads in her textbook.
"I consider it an easier and more efficient way of learning math," she said. "Before it was harder for me to understand and work on problems on my own."