Theresa HarringtonSecond-graders at Aspire Eres school in Oakland work together on math problems.Theresa HarringtonSecond-graders at Aspire Eres school in Oakland work together on math problems.As school districts around California gear up for the next round of testing on Common Core-aligned assessments, educators are hoping that students’ math scores will be higher than they were last year, when the tests were administered for the first time.
Statewide, scores on the Smarter Balanced math tests that over 3 million students took last spring were especially disappointing. Far fewer students scored at a proficient level in math than in English language arts. Forty-four percent of students in grades 3-8 and 11 who took the tests met or exceeded standards in English language arts, compared to 33 percent who met or exceeded the math standards.
RelatedEducators try to come to terms with low math scores on Smarter Balanced testsProficiency in math is a key to advancement after high school, particularly for students seeking admission to California’s four-year public universities. Yet, too often it can be a stumbling block with long-range implications for students’ lives.
But officials in six school districts being tracked by EdSource – as well as the Aspire charter school network – believe they will be able to bump up students’ math scores when the Smarter Balanced tests are administered this spring.
Curriculum experts in Aspire and the Elk Grove, Fresno, Garden Grove, San Jose, Santa Ana and Visalia Unified school districts base their confidence on new curriculum materials they have introduced in classrooms this year, along with ongoing teacher training. In addition, some of the districts have expanded students’ access to technology, such as Google Chromebooks and Wi-Fi, to better familiarize them with the computers they’ll use to take the tests, which they believe will contribute to higher scores.
Last year, students in the Elk Grove, Garden Grove and San Jose districts surpassed the state average of 33 percent meeting or exceeding math standards, while students in Aspire and the Visalia, Santa Ana and Fresno districts scored lower. All were in the process of transitioning to using new curriculum materials, but some didn’t fully introduce them into the classroom until this year.
District leaders in Elk Grove are hoping that their emphasis on professional development for teachers will translate into improved student outcomes.
“Probably our biggest push is on instructional strategies designed to engage all students and encourage dialogue in the classroom,” said Dianne Willson, math program specialist for grades 7-12 in Elk Grove Unified. “We’re gauging whether students are having productive conversations where they are building upon each others’ thoughts and looking at how much time they spend in class talking to each other about math.”
RelatedDistrict officials want to avoid overreacting to new test resultsElk Grove conducted math training for teachers last summer and didn’t really begin implementing its new high school curriculum until this year, Willson said. Through a grant from the S.D. Bechtel, Jr. Foundation, the district has been able to offer ongoing K-8 teacher training in math all year long, she added.
Although the State Board of Education adopted the Common Core standards in 2010, it did not adopt a list of recommended math materials for use in kindergarten through 8th grade until 2014. During that time, many districts scrambled to come up with their own lesson plans and materials aligned to the new standards. Districts were not required to use textbooks and other resources from the state’s list of materials, but if they chose their own they were expected to go through a rigorous process of reviewing materials involving teachers and other district staff.
Most of the districts being tracked by EdSource along with the Aspire charter schools have now chosen which Common Core-aligned math materials to use in their classrooms. Fresno Unified, however, has adopted elementary and middle school materials, but is still reviewing which high school textbooks and supplementary materials it will settle on.
Last year at Garden Grove Unified, groups of elementary teachers were piloting new materials while another group was still using old materials, said Sara Wescott, assistant superintendent for elementary education. Secondary teachers were also using two sets of materials, she said.
“Our math implementation was not consistent across the district, as it always has been done previously,” she said. “The way the state rolled out the Common Core implementation before there were materials (available) was a little bit challenging, to say the least.”
RelatedCurriculum materials a sticking point in Common Core implementationThis year, however, classes throughout the district are using the same sets of materials. All of the curriculum materials adopted by Garden Grove Unified were on the list of textbooks recommended by the State Board of Education. They include: enVisionMATH from Pearson Scott Foresman in grades K-6, Go Math! from Houghton Mifflin Harcourt in middle schools and Glencoe Algebra I by McGraw-Hill. The district is also using manipulatives, such as blocks and Play-Doh, to help students understand math concepts, such as place value and fractions, Wescott said.
“This year, both elementary and secondary teachers all have a new math curriculum,” Wescott said. “In addition, every teacher in the district participated in training in the new textbook prior to school starting.”
Like Elk Grove and Aspire, Garden Grove is emphasizing discussions among students as they work together to solve problems. This collaborative approach to learning is a central principle of the Common Core standards, and educators believe that these deeper discussions in classrooms over the past year will also contribute to students doing better on the tests this spring.
“The kids are really enjoying the opportunity to talk to each other and to also have real-world experience,” Wescott said. For example, some students are learning how to calculate the area of shapes by building them in class out of construction paper or blocks. “So they’re using a lot of different materials they haven’t previously used,” she said.
Similarly, San Jose Unified is shifting from focusing on rote formulas to solve problems characteristic of pre-Common Core math to spending more time developing students’ conceptual understanding of math based on real-world applications, said Jackie Zeller, the district’s director of secondary curriculum, instruction and English learner services. For example, the district’s new SpringBoard mathematics curriculum from the College Board, which it implemented at the secondary level this year, includes a 7th-grade unit that asks students to analyze financial transactions using ratios and proportions, figure out the dimensions of a soccer field, and draw actual structures to scale.
The SpringBoard curriculum requires students to “go through a discovery process as a team,” Zeller said, explaining that classes spend about one-third of their time learning through direct instruction from teachers, one-third of their time in “discovery-based” work and one-third in other group activities. “This type of teaching,” she said, “requires more planning, so it will take teachers a few years to build the skills needed to create new lessons.”
“We are not doing test prep or teaching to the test,” Zeller said in an email. “Good teaching of the standards – including the mathematical practices – should make a difference in our students’ scores.”
Common Core “mathematical practice” standards span all grade levels and are meant to help students understand problems, solve them and explain their reasoning. These are separate from the standards for “mathematical content,” which explain what students are expected to learn at each grade level.
Theresa HarringtonCommon Core “Mathematical Practice” Standards translated into “Student Friendly Language.”In Christine Carucci’s geometry class at Leland High in San Jose, the eight mathematical practice standards appear on a poster that translates them into “student-friendly language”: trying many times to solve a problem; thinking about it first; discussing strategies ahead of time; using symbols and numbers; using pictures, drawings and objects; checking to see if calculations are correct; using current knowledge; and using strategies that have worked with other problems.
Carucci pulled several business cards out of her wallet, then asked her students to determine whether triangular logos from fictitious companies would fit onto business cards, letterhead stationery and advertisements. The teens drew triangles and measured their angles and sides, then discussed how they could be scaled to size. They shared different ways they solved the problems, explaining their strategies and reasoning.
The SpringBoard curriculum requires students to learn by trial and error, instead of by relying on the teacher to explain how to do the problem, Carucci said in an interview after the lesson. But, she said teachers are also learning how to best present the lessons, figuring out what works and what doesn’t with their students.
“We’ve seen a lot of epic fails and we’ve seen a lot of really great lessons,” she said. “Next time, I’ll probably have a couple of students come up to the board and probably have some students show more of their work. After a couple of years, it’s going to be amazing.”
Theresa HarringtonA Leland High School student in San Jose works on a geometry lesson.Still, Carucci said she is already seeing progress, as students are learning to think critically, tackle problems together and persevere.
“They don’t freak out when they see a word problem,” she said. “They don’t just shut down, where in the past they would have.”
Students said they like the class and enjoy hearing their classmates explain the reasoning behind their answers. They also appreciated working on problems that were related to the business world.
“It helps you realize that it really is useful,” said Emmy Mariani, a 15-year-old sophomore. “People always say, ‘You’re going to use this someday.’ Now we can see how.”
Visalia Unified students are learning to work together on problems, but some are still having difficulty figuring out the answers when working individually, said Stacey McNinch-Curschman, the district’s secondary curriculum director. She said students are learning to ask thoughtful questions, critique each other’s thinking, persevere and use multiple problem-solving strategies.
“Those are things we’re seeing more of because we’re staging it in the classroom,” she said. “We’re seeing students in groups being more successful in that process and coming to conclusions. Then, when we separate them and give them a test, that doesn’t always translate. Students are still trying to build that muscle (to do it individually) right now.”
The district has adopted the Glencoe Integrated Mathematics curriculum for high schools and Go Math! for K-8 students.
Although six Santa Ana Unified schools are using Go Math!, the rest are using digital resources and teacher-created lessons almost exclusively to teach math, said Michelle Rodriguez, the district’s assistant superintendent for K-12 teaching and learning. Santa Ana is emphasizing project-based learning by integrating math into real-world problems, she said.
For example, Rodriguez said students in the district’s Advanced Learning Academy – a new charter school focused on project-based instruction emphasizing Science, Technology, Engineering and Math, or STEM, in grades 4-6 this year – completed a project on recycling and conservation that involved composting as a way to reduce waste.
“They used math in that context to estimate how much they would be conserving to support the city of Santa Ana, if we actually did a composting effort,” Rodriguez said. “So, it’s not math for the sake of math, but applying math to a challenging problem.”
Like the other districts, Santa Ana is also focusing on “collaborative academic conversations” between students to help them communicate their reasoning as they tackle problems in math classes.
“What we’ve found is at first it was really hard for our students to explain their thinking because they weren’t really used to having to do that,” Rodriguez said. “They were able to say, ‘The answer is 10,’ but they weren’t used to saying why it’s 10.”
Fresno Unified, where only 18 percent of students in the district met the math standard on the Common Core tests last year, did not have its mathematics curriculum and materials in place last year, said Rosario Sanchez, associate superintendent for curriculum and instruction. The district has adopted “Go Math!” by Houghton Mifflin Harcourt in K-8, but is still reviewing secondary math materials, she said.
“We didn’t start training until late in the summer,” she explained. “Site leaders and instructional coaches are doing classroom walk-throughs to see if we are moving toward the mathematical practices and instructional shifts, utilizing the new resources that we just purchased in mathematics.”
These shifts include pairing students or putting them in small groups to talk about their work, said Tiffany Hill, a Fresno Unified curriculum and instruction administrator.
At Aspire, all schools in the charter system are focusing more this year on reading as a critical skill for math problem-solving, said Elise Darwish, chief academic officer.
“We did some analysis and there’s a clear correlation between reading level and how well students did in math reasoning,” she said. “It’s given us some really clear next steps around reading instruction and reading level.”
Credit: Theresa Harrington/EdSource TodaySecond-grade teacher Mark Montero points to each word as he and students read problems aloud in his 2nd-grade class at the Aspire ERES Academy in Oakland.On a recent afternoon, Mark Montero, a 2nd-grade teacher at Aspire ERES Academy in Oakland, pointed to each word as he read it aloud with his class to ensure students understood the vocabulary. He and other Aspire teachers encourage students to “self-assess” whether they understand problems or need help. Then students who have mastered the concept that day pair up with others who need help.
“They’ve been exposed to Common Core math since kindergarten, so they haven’t been taught the other way,” Montero said. “I don’t think these kids will ever say to their friends, ‘You’re wrong.’ They explain their thinking and come to a common solution.”
Students in Mark Montero’s 2nd-grade class at the Aspire ERES Academy charter school in Oakland are eager to share their math problem-solving skills with each other. After Montero and his students read problems aloud together recently, students took turns showing the rest of the class their strategies for figuring out the answers.
For example, 7-year-old Fernando Munoz explained to his classmates how he solved the equation 15 – 6 = 9. Fernando said he knew that 6 was made up of 5 + 1, so he first subtracted 5 from 15 to get 10, then subtracted 1 to end up with 9.
Montero gave Fernando a “high five,” then made a note on the equation showing the rest of the class the boy’s thinking, by indicating that 6 is the same as 5 +1. The teacher and his students then reviewed some other strategies for finding the answer, such as counting backwards on a number chart or counting on their fingers.
Theresa HarringtonSecond-grader Fernando Munoz solves a subtraction problem at Aspire ERES school in Oakland.
Similar interactions between teachers and students are happening across the state, as educators seek to engage their classes in discussions about the reasoning and critical thinking involved in math, based on the Common Core State Standards. These types of “number talks” are helping to prepare students for Smarter Balanced testing this spring, which will be administered to students in grades 3-8 and 11 in math and English language arts.
“There’s not one right method,” Montero said in an interview after the lesson. “The Common Core is all about exposure to different tools.”
Fernando said he enjoys solving problems.
“I like math,” he said, “because I get to use my brain and get smarter, so I can be a scientist.”
** The state did not recommend texts for math beyond Algebra I.
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