Many accomplished teachers are enthusiastic about the common-core math standards’ emphasis on mathematical reasoning and strategic expertise over rote computation, but some say the transition to the new framework poses daunting challenges for students who are already behind in the subject.
“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 Intermediate School 52 in New York. 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 Core State Standards. More than half 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 struggling students make the shift to the new instructional paradigm.
One approach teachers commonly cite, 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.
For more stories on teachers’ efforts to adapt to the common standards, see Education Week Teacher‘s new online package, “Common-Core Instructional Opportunities.”
“It’s OK if you need to start more basic,” said Mr. Arcos, explaining that initially he used two-digit addition without regrouping 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. He 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 1 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.
Mr. 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 providing demonstrations of solutions and bridging new concepts to students’ prior knowledge.
“You have to help kids understand how to justify solutions, through discussion, interaction, and close guidance,” said Mr. 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, Mr. 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, Mr. 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,” Mr. 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 understanding 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.” That 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.
Mr. 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, Mr. Minkel said.
‘Harder to Teach’
While some math teachers working with struggling students are finding ways to adapt their instruction to the common standards, 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 Mr. Minkel. “It forces you to go deeper. In the end, teachers have to get better at math.”
The 2007 state teacher of the year in Arkansas, Mr. Minkel said he feels fortunate that his school switched to a common-core-like math approach several years ago, smoothing the transition by hiring an on-site 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.”
Mr. 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.
At this stage, Mr. Vilson lamented, 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 be given in the 2014-15 school year. “Even with the understanding I may have acquired,” he said in an email, “I still feel that I don’t know much … because of the assessments.”
Coverage of “deeper learning” that will prepare students with the skills and knowledge needed to succeed in a rapidly changing world is supported in part by a grant from the William and Flora Hewlett Foundation, at www.hewlett.org.
A version of this article appeared in the March 27, 2013 edition of Education Week as Math Teachers Break Down Standards for At-Risk Students