Big Shifts Ahead for Math Instruction
Teacher Nena Hupp reads the book 1+1=5 and Other Unlikely Additions to children in her kindergarten class at Worthington Elementary.
—Stephen Voss for Education Week
Some topics will be introduced earlier, some omitted, and students will have to show their understanding
Ellicott City, Md.
Nena F. Hupp pauses from reading her kindergartners the picture book Let's Count to help them better understand the math assignments they are about to tackle in small groups.
"Remember, when you get to 10 dots, a better way is to represent those 10 dots with just a stick," said Ms. Hupp, who teaches at Worthington Elementary School in this community near Baltimore. "It takes us forever to have to count all those dots. Mathematicians were smart when they came up with that idea, because it makes it so much easier."
Prior to this school year, kindergartners in the 50,000-student Howard County district—and in public schools across Maryland—were not expected to learn about representing tens and ones, a building block for understanding place value, explains Kay B. Sammons, the district's elementary-math coordinator.
"Prior to the common core," she said, "it was a 1st grade objective."
That's now changing, along with a whole lot more.
Across the nation, big shifts are afoot as 45 states and thousands of school districts gear up to implement the Common Core State Standards in mathematics. The standards will change the grade levels at which some content is introduced, push aside other topics altogether to achieve greater depth, and ask students to engage in eight "mathematical practices" to show their understanding, from making sense of problems to reasoning abstractly and constructing viable arguments.
Some districts are already working hard to make the transition.
In Albuquerque, N.M., more than three dozen 4th and 8th grade math teachers are piloting the new standards this school year. In fact, several of them starred in videos recorded last fall in their classrooms to demonstrate lessons.
In Boston, teams of teachers and teacher-leaders are developing new curriculum-guidance documents, grade by grade, and combing through the district's textbooks and other instructional materials to see how they fit with the common core, what's useful, what's not, and where material should be reordered or supplemented.
In Howard County, the math standards were inaugurated for kindergarten this school year, with the 1st and 2nd grades to follow in the fall. To help prepare, district math leaders brought together some teachers, including Ms. Hupp, to serve in a focus group that delivered feedback on draft curricular materials for kindergarten.
"We would create things and get reactions from the teachers, asking: 'Does this make sense to you? Would you change this?' " said Ms. Sammons. "They gave us some terrific insights into how to develop this tool that is useful and user-friendly."
The suburban district also has started to communicate with families, whether at back-to-school events, in newsletters, or on the district website, to make sure they understand the changes coming. In fact, the district is planning a broader public relations campaign, with brochures, public forums, local TV spots, and even podcasts.
Gail F. Burrill, an academic specialist at Michigan State University and a former president of the National Council of Teachers of Mathematics, suggests that bringing families on board is critical.
"It's not going to be enough just to support the teachers in making this change," she said, "if the broader community doesn't understand and support it."
'Flipping a Switch'
States and districts face a host of challenges in adapting to the standards, from ensuring that teachers are adequately prepared and supported to overhauling the curriculum and, more broadly, figuring out exactly what exemplary classroom practices tied to the standards should really look like.
The transition is tricky since, even as districts are beginning to move toward the new standards, common assessments pegged to them have yet to be developed. District officials note that, for the time being, schools will be judged on existing state tests that don't align to the new standards.
Meanwhile, many state and district officials say textbook publishers are scrambling to catch up with the common standards and few, if any, materials that truly align are available.
In addition, it's not simply a matter of flipping a switch to have instruction at all grade levels reflect the new standards. After all, a lot of math content builds on prior learning.
"You can't say, from one year to the next, we're going to go 100 percent common-core standards, because students aren't coming with the [prior knowledge] to embrace it," said Jesch A. Reyes, the director of math and science for the 405,000-student Chicago district, which has a group of "early adopter" schools in which teachers are starting to implement the new standards and share lessons learned. "Over the next several years, we're ... introducing them incrementally, building teacher capacity and student capacity."
Standards for Mathematical Practice
The common standards in mathematics do not simply address academic content. They also outline a set of eight Standards for Mathematical Practice, which describe ways in which students ought to engage with the subject matter as they grow in mathematical maturity and expertise throughout the school year.
- Make sense of problems and persevere in solving them.
- Reason abstractly and quantitatively.
- Construct viable arguments and critique the reasoning of others.
- Model with mathematics.
- Use appropriate tools strategically.
- Attend to precision.
- Look for and make use of structure.
- Look for and express regularity in repeated reasoning.
Many district and state officials say they expect, to varying degrees, that the new standards will be tougher for students to meet.
William Barnes, the Howard County district's secondary-math coordinator, describes the new standards as "very different" and "much more rigorous" than Maryland's prior math standards.
"This is fewer, higher, so that's a significant shift in paradigm for Maryland," said Mr. Barnes, the immediate past president of the Maryland Council of Teachers of Mathematics.
On average, students will be expected to master about half as many standards as before, he said, but they'll be asked to understand that content in much greater depth.
"Here in Illinois, a lot of the content taught at each grade level is being pushed down to other grade levels, even several grades down," said Mr. Reyes from the Chicago school system.
His colleague, district math specialist Matthew S. McLeod, adds that while many teachers in the city's early-adopter schools seem enthusiastic about aspects of the standards, such as the eight mathematical practices that are a key focus of their work right now, the teachers are apprehensive about the new expectations.
"They are panicked about how hard it's going to be to get our students to this level of rigor," he said.
An array of initiatives have emerged to ease the transition to the new standards. For one, the 11 states, plus the District of Columbia, that won a slice of $4 billion in federal Race to the Top aid have had extra money to fuel professional development and devise new resources to help schools, among other activities.
Advisory Group
Meanwhile, a set of leading national groups, including the NCTM, the Association of State Supervisors of Mathematics, and the Council of Chief State School Officers, have formed the Math Common Core Coalition to offer expertise and advice on the standards.
One new resource touted by several math educators is the Illustrative Mathematics Project website, which aims to supply high-quality math tasks, all carefully vetted by math experts and teachers, to illustrate the range and types of work that students will experience in a "faithful" execution of the standards.
William G. McCallum, a University of Arizona math professor who spearheaded the project and also was a lead writer of the common standards, said plans are in the works to expand the site to become a thriving online community of math educators with expertise in the new standards and how to translate them for the classroom.
'Stronger Foundation'
The Howard County district, one of Maryland's top-performing school systems, is working on many fronts to implement the standards, from providing professional development to revamping its curriculum, in an effort to be sure schools are ready for all the changes to the what, when, and how of math instruction envisioned with the common core.
On the when issue, for example, Mr. Barnes said about 40 percent of concepts now taught in Algebra 2 will shift to Algebra 1.
At kindergarten, the only grade level where the district has fully implemented the standards, the core focus is number development and spatial thinking.
"The children will have a stronger foundation in number as they move into 1st grade than they historically did," said Ms. Sammons, the elementary-math coordinator.
In the past, for instance, kindergartners were expected to be able to count up to 31, by ones; the new standards ask them to count to 100, by both tens and ones. In addition, she said, they are asked to start counting from any number.
The district has a three-year transition plan, she said, so that by 2013-14 all grade levels will fully reflect the new standards.
It is developing a detailed curriculum—described as a set of "living documents"—that will evolve and grow to meet the needs of educators and students.
The material, posted on a wiki site, walks Howard County teachers through the math standards one by one. First, the standard is presented. Then, the district translates it into plain language with further explanation for teachers. The wiki site identifies common student misconceptions to watch out for, provides a sequence map of the curriculum and a progression chart to help see where students need to be, with benchmarks along the way. It also identifies a host of instructional resources, as well as information on formative and summative assessments.
Nena Hupp helps Chase Toler in her class at Worthington Elementary School. Students in the Howard County, Md., district are being taught math concepts at an earlier age.
—Stephen Voss for Education Week
"We really unpack what's supposed to be going on in the standards," said Ms. Sammons.
Ms. Hupp, one of three kindergarten teachers at Worthington Elementary, raves about the wiki site, saying it's a vital resource. Overall, she's upbeat about the new standards and her experience so far teaching them.
"I like it so much better," said Ms. Hupp, a 15-year teaching veteran who notes that she is now better able to meet individual children where they are academically.
One big challenge, she said, is figuring out how to reach the deeper level of math understanding the standards espouse.
"The question is: How do you dig deeper?" she said. "For anybody who starts teaching the common core, that is going to be the challenge."
But the wiki guidance has been helpful in identifying sample lessons to foster that, she said.
One especially welcome change, she said, is that with fewer math concepts to cover, she has time to better gauge whether a student truly understands the material.
"Some of the kids that [met] the standard at the surface level were missing some pieces," she said. "You could start picturing what their knowledge of that skill is, whether it was just memorization or whether they had it."
A Taste of Common Core
Meanwhile, with support from the Seattle-based Bill & Melinda Gates Foundation, a handful of urban districts have gotten started on implementing the common core. Six systems, including Albuquerque and Boston, received $500,000 planning grants in 2010. Those six, along with two others, are also "lead districts" in a common-standards project of the Council of the Great City Schools, which received a $4.6 million grant from Gates last year for its work. (The Gates Foundation also provides support for coverage of K-12 business and innovation in Education Week.)
The pilot project in the Albuquerque school system is mainly aimed at testing approaches to support teachers and schools in implementing the standards in math and English/language arts, from their use of classroom materials and new curriculum maps to administering periodic student assessments and the delivery of professional development.
"The goal was for them to be able to get a taste of the common-core implementation and for us to get feedback so that we know how we should go about this districtwide, what worked, what didn't," said Gina Middleton, who is managing the district's pilot program.
She's heard a lot of positive feedback from educators.
"What they love, love, love is ... giving the depth to content and not teaching so much of the breadth," said Ms. Middleton, "so there are less standards, but they are dense, very compact."
Holly D. Zaluga-Alderete, a math teacher in the city's Polk Middle School, echoes that point.
"I don't have a mile-long list of standards to cover," she said. "For example, with the Pythagorean theorem, in the past, we would say, 'This is the Pythagorean theorem and how we use it' and move on. This year, we could get in depth, how it worked, the ins and outs ... and knowing the whys."
She added: "It's a lot more rewarding and letting me be a teacher."
One big concern among participating teachers, said Ms. Middleton, is the lack of resources to show them what the standards should look like in the classroom.
"Teachers have been craving to see it in action," she said.
As one remedy, several math teachers, including Ms. Zaluga-Alderete, agreed to step in front of a camera to demonstrate lessons. In Boston, a top priority is "organizing and sequencing the curriculum," said Linda P. Chen, the 57,000-student district's deputy chief academic officer.
The district named teams of math teachers and teacher-leaders at every grade level. Those work groups recently began sitting down with the state's version of the common standards to redesign curriculum-guidance documents.
"Their charge is to become experts with the [new standards] and to use this expert knowledge to assist" the district in overhauling its curriculum, said Christine M. Hall, the school system's senior director of secondary math.
By early June, each group is to complete work on a set of documents that identify the "scope and sequence" of instruction for their grade level, detailing the standards to be taught in each unit and the time spent on them. Also, each group will provide exemplars of problem types to use in class, as well as sample tasks, to illustrate the math comprehension that should be evident throughout the year, said Ms. Hall.
"Our goal is ... that teachers can leave for their summer vacation with something in hand that clearly articulates the major shifts of the curriculum under the common core," she said. "While there are major shifts, this will be a fluid process, because you can't just say we're going to teach 6th grade anew, you need to attend to the transition."
The work groups also are poring over the district's current textbooks and other classroom materials "with a very critical eye, saying, 'We know we have this, we know what we are being called to teach,' " Ms. Hall said. "How do we selectively choose the problems and questions in our textbook? How do we perhaps rephrase introductions to lessons, how do we reorganize lessons in units to attend to the new focus and coherence of the common core? This is a work in progress."
Indeed, Ms. Chen, the deputy chief academic officer, said that her district, like some other large urban systems, is holding off on buying new textbooks because of budget constraints and because publishers still have work ahead.
"There really, truly is not something out there that you can buy that is aligned," Ms. Chen said.
Just Do It
Although many educators say it's a daunting task before them to feel prepared for the common standards, Ms. Hupp from Worthington Elementary said the key is just to plunge ahead.
"We're feeling so much better about it," she said of the school's kindergarten team. "With anything new, you're going to feel a lot of anxiety. ... The only way you can feel good about something is actually diving in and doing it."
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