The Common Core State Standards for mathematics, now being introduced in schools across the country, set new grade-by-grade expectations for deepening students’ understanding of math concepts, with an emphasis on algebraic thinking.
But while many accomplished math teachers are enthusiastic about the standards’ emphasis on mathematical reasoning and strategic expertise over rote computation, some say the transition to the new framework poses daunting challenges for students who are already behind in math.
“Every time I talk to other teachers, this issue comes up,” said Silvestre Arcos, the founding math teacher at KIPP Washington Heights Middle School, a charter school in New York City. “The big question is, how do we build up these advanced skills with kids who come in behind?”
Students need “prerequisite knowledge” to meet the new grade-level expectations mapped out in the common standards, said José Vilson, who teaches 8th grade math at I.S. 52, a public middle school a in New York City’s Inwood neighborhood. But by the time they reach him, students at his school—many of whom are English-language learners—often “have a lot of catching up to do,” he said.
Such observations appear to reflect broader professional concerns about the common standards. More than half of the respondents in a recent survey of K-12 teachers who are registered users of edweek.org said they feel unprepared to teach the common standards to high-needs students.
Despite often lacking support and clear guidance, however, teachers aren’t necessarily ready to throw in the towel. Some math educators are taking steps to refine their practices and adopt creative methods to help at-risk and struggling students make the shift to the new instructional paradigm.
One approach commonly cited by teachers, for example, is to maintain the common core’s emphasis on abstract reasoning and conceptual understanding while, at least at first, using word problems that require less advanced math skills.
“It’s OK if you need to start more basic,” said Arcos, explaining that at first he used two-digit addition without regrouping with his 5th graders, many of whom were at a 2nd or 3rd grade level in math.
The key is to “avoid focusing on the algorithm or any tricks,” he said, so that the students have to work through the problems strategically. Arcos noted that students at his school have daily problem-solving classes in this vein, as well as computation-skills practice two mornings a week.
Similarly, Todd Rackowitz, a math teacher at Independence High School in Charlotte, N.C., noted that, in integrating the common standards into an Algebra I course for students who are behind grade level, he “focuses on problems that don’t involve complex computation at first.” Even using basic math, students can begin to “make connections between the key elements of algebra, like slope and parallel lines and rate of change,” he said.
Eighth grade teacher Vilson said that he, too, has had “to integrate prior [grade-level] skills into problems,” adding that this can require “a lot of interpretation” of the standards, curriculum materials, and expectations for assessments. “There’s some guesswork involved,” he acknowledged.
Teachers introducing the common standards in math into classes with high numbers of at-risk or behind-grade-level students also frequently speak about the need for “modeling” and “scaffolding,” highlighting the importance of intentional instructional support.
“You have to help kids understand how to justify solutions, through discussion, interaction, and close guidance,” said Arcos, adding that his school has adjusted scheduling to allow for more small-group and one-on-one instruction in math.
Since many of the students at his school struggle with English-language and literacy issues, Arcos often focuses on building their close-reading skills as part of math instruction, helping them break apart the text of word problems and annotate the sentences. He has found that allowing the students to draw model representations of word problems and collaborate on solutions can also be helpful.
When his students are struggling with a problem or new concept, Arcos said, he demonstrates how to work through similar problems and discusses his reasoning with them.
“You never want to pass up an opportunity to really teach,” Rackowitz said of his like-minded approach. “If a student is struggling, you want to give them a start and talk him through it while letting him work it out. Provide scaffolding in terms of understanding the problem and possible approaches, offering progressively less and less.”
To build students’ problem-solving and abstract–reasoning skills, he has also found it helpful to have students work out solutions and understandings through “group discussion and discovery.”
To spark engagement with problems, Justin Minkel, a 2nd and 3rd grade teacher at Jones Elementary School in Springdale, Ark., noted that he has his students “do a lot of writing in math.” This practice, he said, helps students see the conceptual underpinnings of the problems they are working on and, with his assistance, see how words and phrases can relate to mathematical notations.
Minkel, whose school has a high percentage of low-income students, said he also makes an effort to give his students problems that have “practical applicability” to the real world. He noted that he has had success, for example, in having his students use what they were learning in math in an economics unit that involved determining the costs of materials for a building project against a budget.
Such activities can help students “make sense of problems"—the first of the common core’s Standards for Mathematical Practice—and begin thinking about the ways math relates to their own lives, Minkel said.
Arcos advocates that approach as well. “If you’re going to teach decimals,” he stated, “do it with real-world, authentic problems.”
‘Harder to Teach’
While some math teachers working with struggling students are finding ways to adapt their instruction to the common standards, however, they still point to the need for additional training and professional development in the field.
“It’s harder to teach this way than just teaching algorithms and steps,” said Minkel. “It forces you to go deeper. In the end, teachers have to get better at math.”
Minkel, the 2007 State Teacher of the Year in Arkansas, said he feels fortunate in that his school switched to a common-core-like math approach several years ago, smoothing the transition by hiring an onsite math coach and providing regular job-embedded professional development. “She talked through a lot of the questions I had,” he said of the coach. “Sometimes we realize that we don’t understand things as well as we thought.”
Rackowitz, a National Board-certified teacher, noted that he has jumped at every common-core-oriented professional development opportunity that has come his way, but still feels he needs additional training to break old habits and become more adept at helping his students adjust to new methodologies. “I need more [work] on coming up with these mathematical-discovery activities and finding creative ways not just to teach the algorithm, since that’s the way I learned,” he said.
Vilson lamented that, at this stage, teachers’ efforts to adjust to the new framework are complicated by the uncertainty surrounding the makeup of the common-core-aligned assessments, which are scheduled to go into effect in 2014-15. “Even with the understanding I may have acquired, I still feel that I don’t know much … because of the assessments,” he said in an email.